Study shows exponential growth of Laplacian determinant on random hyperbolic surfaces.
problem Understanding the behavior of Laplacian determinants on random hyperbolic surfaces.
method Investigated various models of random hyperbolic surfaces and their Laplacian determinants as genus increases.
result For all popular models, the determinant grows exponentially with a universal exponent as the genus goes to infinity.
Data describing historical economic growth are analysed. Included in the analysis is the world and regional economic growth. The analysis demonstrates that historical economic growth had a natural tendency to follow hyperbolic distributions. Parameters describing hyperbolic distributions have been determined. A search …
New method calculates growth rates of Artin-Tits monoids, linking to partial theta function.
problem Growth rates of Artin-Tits monoids and their connection to partial theta function.
method Determining growth functions using simple matrix determinants and atomic generators.
result Exponential growth rates of Artin-Tits monoids of type An tend to 3.233636... as n increases. We determine the distribution of size and growthrates of German business firms in 1987-1997. We find a log-normal size distribution. The distribution of growth rates has fat tails. It can be fitted to an exponential in a narrow central region and is dominated by finite-sample-size effects far in its wings. We study the…
We consider the maximization of the long-term growth rate in the Black-Scholes model under proportional transaction costs as in Taksar, Klass and Assaf [Math. Oper. Res. 13, 1988]. Similarly as in Kallsen and Muhle-Karbe [Ann. Appl. Probab., 20, 2010] for optimal consumption over an infinite horizon, we tackle this pro…
Growth rate of the world Growth Domestic Product (GDP) is analysed to determine possible pathways of the future economic growth. The analysis is based on using the latest data of the World Bank and it reveals that the growth rate between 1960 and 2014 was following a trajectory approaching asymptotically a constant val…
Study subgroup growth in RAAGs and RAAGs with Coxeter relations.
problem Understanding subgroup growth in RAAGs and RAAGs with Coxeter relations.
method Analyzing the independence number of defining graphs for RAAGs and conjecturing for RAAGs with Coxeter relations.
result Subgroup growth rate depends on the independence number of the defining graph for RAAGs and a conjecture for RAAGs with Coxeter relations.
This paper calculates the stock price covariance with correlated growth rates.
problem Determining the covariance of stock prices with correlated growth rates.
method Developed a formula for the covariance of random stock prices with correlated growth rates of dividends.
result A formula for the covariance of stock prices with correlated growth rates of dividends.
Study growth rates of subgroups in groups with a constricting element.
problem Understanding growth rates of subgroups in groups with a constricting element.
method Examining the spectrum of relative and quotient exponential growth rates of quasi-convex subgroups.
result Determine when growth rates of subgroups are strictly smaller or coincide with the group's growth rate.
Graph complexity and Mahler measure linked through spanning trees.
problem Linking graph complexity and Mahler measure.
method Analyzing spanning trees and Mahler measure of Laplacian polynomials.
result Growth rates of Mahler measure are asymptotic to log(2d) for grid graphs.
Estimates growth loss in fund models and proposes a shrinkage method.
problem Estimating growth loss in fund models under frequentist and Bayesian estimation.
method Proposes a shrinkage method to target maximal growth with minimal deviation.
result Empirical evidence shows shrinkage gives a stable estimate closer to growth potential.
New growth functions for mapping class sets discovered.
problem Growth of mapping class sets in terms of Lipschitz maps.
method Different mechanism to show variety of growth functions.
result Universe of possible growth functions is large.
Classifies gravitational instantons with quadratic volume growth.
problem Classifying gravitational instantons with specific growth properties.
method Proves a classification theorem for ALG∗ gravitational instantons, determines topology, and proves existence of uniform coordinates. result Proves a relationship between ALG gravitational instantons of different orders.
We investigate the relation between economic growth and equality in a modified version of the agent-based asset exchange model (AEM). The modified model is a driven system that for a range of parameter space is effectively ergodic in the limit of an infinite system. We find that the belief that "a rising tide lifts all…
In this paper, we consider the formal power series whose n-th coefficient is the number of copies of a given finite graph in the ball of radius n centred at the identity element in the Cayley graph of a finitely generated group and call it the growth function. Epstein, Iano-Fletcher and Uri Zwick proved that the growth…
Optimizes dimension estimate for holomorphic functions on Kähler manifolds.
problem Determining the optimal dimension for holomorphic functions with polynomial growth.
method Analyzes Kähler manifolds with non-negative holomorphic bisectional curvature.
result Identifies the specific gap and optimal dimension for maximal volume growth.
Paper proves stability of volume conjecture under cabling.
problem Stability of volume conjecture under cabling.
method Analyzes Turaev-Viro invariants and simplicial volume.
result Stability of Chen-Yang conjecture under (2n+1,2)-cabling. This paper presents a general solution for a recent model by Keen for endogenous money creation. The solution provides an analytic framework that explains all significant dynamical features of Keen's model and their parametric dependence, including an exact result for both the period and subsidence rate of the Great Mo…
Study predicts U.S. county COVID-19 growth using demographic and social distancing data.
problem Predicting county-level COVID-19 growth during the pandemic.
method Spectral clustering, correlation matrix, demographic features, social distancing scores, LSTM model.
result Effective prediction of future county growth using demographic and social distancing data.
Survival strategies in a market with self-determined prices are closely tied to log-optimal investment.
problem Survival of wealth in a market with endogenous prices.
method Assume only one's actions affect prices, use log-optimal strategy, disregard actual prices.
result Survival strategies are asymptotically close to log-optimal strategies.
Study measures economic growth sources in Iran's mining sector using neoclassical growth accounting.
problem Determining the share of economic growth sources in Iran's mining sector.
method Neoclassical growth accounting approach, using production function and Solow residual equation.
result Average annual growth rate of TFP was 2.94% over 30 years.
The paper defines higher invariants for groups of polynomial growth and proves their convergence.
problem Defining and proving convergence of higher invariants for groups of polynomial growth.
method Using delocalized cyclic cocycles and a determinant map construction.
result A well-defined pairing between delocalized cyclic cocyles and K-theory classes of C*-algebraic secondary higher invariants.
We investigate the growth optimal strategy over a finite time horizon for a stock and bond portfolio in an analytically solvable multiplicative Markovian market model. We show that the optimal strategy consists in holding the amount of capital invested in stocks within an interval around an ideal optimal investment. Th…
Study shows exponential growth of knot polynomial tied to Chern-Simons invariant.
problem Asymptotic behavior of colored Jones polynomials of figure-eight knot.
method Analyzes growth rate of polynomial evaluated at specific points.
result Growth rate determined by Chern-Simons invariant of an affine representation.
Given an automorphism of a free group Fn, we consider the following invariants: e is the number of exponential strata (an upper bound for the number of different exponential growth rates of conjugacy classes); d is the maximal degree of polynomial growth of conjugacy classes; R is the rank of the fixed subgrou…
The paper gauges AGI's impact on GDP growth using mathematical metrics.
problem Determining the economic effect of AGI on GDP growth.
method Analysis of historical data, development of a new mathematical algorithm, regression analysis.
result There is a positive correlation between AGI growth and real GDP growth.
The paper introduces Poincaré profiles for metric spaces and groups, linking them to conformal dimension.
problem Understanding the properties of metric measure spaces and groups with polynomial growth.
method Introducing and analyzing Poincaré profiles for groups and hyperbolic spaces.
result Connection between Poincaré profiles and conformal dimension, leading to non-existence of coarse embeddings.
We analyse the asymptotical growth of Vassiliev invariants on non-periodic flow lines of ergodic vector fields on domains of R3. More precisely, we show that the asymptotics of Vassiliev invariants is completely determined by the helicity of the vector field. As an application, we determine the asymptotic Alexander…
Paper classifies economic states and optimizes portfolios for stagflationary environments.
problem Economic uncertainty and stagflationary conditions.
method Mathematical techniques for analyzing multivariate time series, economic driver analysis, self-similarity identification, and portfolio optimization.
result Constructs economic state classifications and computes economic state integrals.
The paper proposes a method to determine the geometric priors of relational data.
problem Identifying geometric structure in heterogeneous, high-dimensional data.
method Combinatorial approach analyzing nearest-neighbor structures and local neighborhood growth rates.
result The method can identify the geometric priors of suitable embedding spaces for relational data.
Investigates the relationship between US money supply and asset indices over 2001-2019.
problem Determining the relationship between US money supply and asset indices growth.
method Information entropy methodology applied to US asset indices (Property, Russell 2000, S&P 500, NASDAQ) over 2001-2019.
result Growth in US broad money supply is the main determinant of US asset indices growth, especially the NASDAQ and Russell 2000.
RELTA-SGLD stabilizes nonconvex SGLD updates with a lighter taming scheme.
problem Stabilizing superlinear stochastic-gradient updates in nonconvex optimization.
method Threshold-based taming with relative-growth principle for stability.
result Polynomial moment stability and first-order stationary accuracy in nonconvex SGLD.
The paper studies random covers of torus knot complements and their statistical properties.
problem Understanding the statistical behavior of finite covers of torus knot complements.
method Asymptotic subgroup growth analysis and Benjamini-Schramm limit theorems.
result Determination of the linear growth rate of Betti numbers for random covers of torus knot complements.
Random surfaces' diameter grows logarithmically with size.
problem Estimating the diameter of random hyperbolic surfaces.
method Uniform gluing of triangles, compactification, asymptotic analysis.
result The diameter is asymptotic to 2logn. Analyzes long-term growth rate of leveraged ETFs using martingale extraction.
problem Determines long-term growth rate of leveraged ETFs under various models.
method Develops analytical approach using martingale extraction and eigenpair of infinitesimal generator.
result Derives explicit long-term growth rates for different reference asset models.
The study calculates the growth rate of reciprocal hyperbolic elements in Hecke groups.
problem Counting reciprocal hyperbolic elements in Hecke groups.
method Analyzes conjugacy classes of hyperbolic elements associated with reciprocal geodesics.
result Determines the asymptotic growth rate and limiting constant of primitive conjugacy classes of reciprocal hyperbolic elements.
Study on k-surfaces in negatively curved 3-manifolds, focusing on energy and entropy.
problem Understanding the growth rate and asymptotic behavior of k-surfaces in negatively curved 3-manifolds. method Proved results on the asymptotic behavior of high energy k-surfaces, including upper bounds and rigidity theorems. result Determined a rigid upper bound for the growth rate of quasi-Fuchsian k-surfaces in negatively curved 3-manifolds. New method uses resurgent analysis to determine growth rate of quantum field theory coefficients.
problem Determining the growth rate of quantum field theory coefficients.
method Resurgence analysis on the Stokes line, leading to transseries decomposition and continued across natural boundary.
result Essential exponent of growth has Cardy-like interpretation as effective central charge.
Improved growth strategies by incorporating stochastic factors in asset returns.
problem Drift uncertainty in asset returns makes growth optimization strategies sensitive.
method Study robust growth-optimization in high-dimensional incomplete markets under drift uncertainty and ergodicity.
result Utilizing stochastic factors improves robust growth rates and optimal strategies.
We present a novel methodology to determine the fundamental value of firms in the social-networking sector based on two ingredients: (i) revenues and profits are inherently linked to its user basis through a direct channel that has no equivalent in other sectors; (ii) the growth of the number of users can be calibrated…
We introduce the notion of spectral flow along a periodic semi-Riemannian geodesic, as a suitable substitute of the Morse index in the Riemannian case. We study the growth of the spectral flow along a closed geodesic under iteration, determining its asymptotic behavior.
Study analyzes GDP growth of CEE countries using time-varying coefficients.
problem Understanding GDP growth patterns of CEE countries post-integration.
method Panel regression with time-varying coefficients.
result Private debt plays a crucial role in economic growth.
The true probability of a European call option to achieve positive return is investigated under the Black-Scholes model. It is found that the probability is determined by those market factors appearing in the BS formula, besides the growth rate of stock price. Our numerical investigations indicate that the biases of BS…
Geometric model predicts unique, smooth ooid shapes.
problem Understanding the unique shapes of ooids formed by carbonate particles.
method Investigating planar curve evolution under a nonlocal geometric equation, demonstrating unique, time-invariant shapes.
result The model predicts a unique, time-invariant, smooth shape for ooids, agreeing with natural observations.
We consider the problem of finding optimal strategies that maximize the average growth-rate of multiplicative stochastic processes. For a geometric Brownian motion the problem is solved through the so-called Kelly criterion, according to which the optimal growth rate is achieved by investing a constant given fraction o…
The paper studies proper discontinuity of actions on Weyl chamber flow spaces.
problem Properly discontinuous actions on Weyl chamber flow spaces for transverse subgroups.
method Analyzes limit sets and quotient spaces, introduces growth indicators and conformal measures.
result Establishes ergodic dichotomy for Weyl chamber flow and introduces new measures.
Model analyzes inventory growth cycles with debt-financed investment.
problem Understanding inventory growth cycles in economies with debt financing.
method Continuous-time stock-flow consistent model for inventory dynamics.
result Model reveals Kitchin cycles in short-run dynamics.
New model predicts grain boundary migration in metals.
problem Anisotropic grain boundary migration in polycrystals.
method Level set-finite element formulation based on thermodynamics and mechanics.
result First analytical solution for anisotropic grain boundary configurations.